# Neural Network Field Theory at Finite Width

arXiv: https://arxiv.org/abs/2608.21588 · HTML: https://mlsanity.com/paper/2608.21588/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Building Quantum Field Theories Out of Neurons](https://mlsanity.com/paper/2112.04527/) (2021)
- [Neural Network Field Theories: Non-Gaussianity, Actions, and Locality](https://mlsanity.com/paper/2307.03223/) (2023)
- [Quantum Mechanics and Neural Networks](https://mlsanity.com/paper/2504.05462/) (2025)
- [Neural network representation of quantum systems](https://mlsanity.com/paper/2403.11420/) (2024)
- [Virasoro Symmetry in Neural Network Field Theories](https://mlsanity.com/paper/2512.24420/) (2025)
- [Topological Effects in Neural Network Field Theory](https://mlsanity.com/paper/2604.02313/) (2026)

## Abstract (arXiv)

Under mild assumptions, any quantum mechanical (QM) model or quantum field theory (QFT) admits a representation in terms of an ensemble of neural networks with countably many random parameters. We investigate the features of NN-QM and NN-FT models with finitely many parameters, such as a feedforward network of width N < ∞. We find that, generically, such models must violate one of the properties of conventional Euclidean QFTs, such as reflection positivity or cluster decomposition. We present several complementary ways of understanding which features can and cannot be preserved at finite N, both in QM and in QFT.